Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Supersymmetric Solution Of Gauge Hierarchy Problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.

Quasi-2D XY Magnetic Properties and Slow Relaxation in a Body Centered Metal Organic Network of [Co-4] Clusters

Octahedral Co2+ centers have been connected by mu(3)-OH and mu(2)-OH2 units forming [Co-4] clusters which are linked by pyrazine forming a two-dimensional network. The two-dimensional layers are bridged by oxybisbenzoate (OBA) ligands giving rise to a three-dimensional structure. The [Co-4] clusters bond with the pyrazine and the OBA results in a body-centered arrangement of the clusters, which has been observed for the first time. Magnetic studies reveal a noncollinear frustrated spin structure of the bitriangular cluster, resulting in a net magnetic moment of 1.4 mu B per cluster. For T > 32 K, the correlation length of the cluster moments shows a stretched-exponential temperature dependence typical of a Berezinskii-Kosterlitz-Thouless model, which points to a quasi-2D XY behavior. At lower temperature and down to 14 K, the compound behaves as a soft ferromagnet and a slow relaxation is observed, with an energy barrier of ca. 500 K. Then, on further cooling, a hysteretic behavior takes place with a coercive field that reaches 5 Tat 4 K. The slow relaxation is assigned to the creation/annihilation of vortex-antivortex pairs, which are the elementary excitations of a 2D XY spin system.

Boundary layer transition observations on a body of revolution with surface heating and cooling in water

Boundary layer flow visualization in water with surface heat transfer was carried out on a body of revolution which had the predicted possibility of laminar separation under isothermal conditions. Flow visualization was by in-line holographic technique. Boundary layer stabilization, including elimination of laminar separation, was observed to take place on surface heating. Conversely, boundary layer destabilization was observed on surface cooling. These findings are consistent with the theoretical predictions of Wazzan et al. in The stability and transition of heated and cooled incompressible laminar boundary layers, in Proceedings of the Fourth International Heat Transfer Conference, Vol. 2, FCI 4. Elsevier, Amsterdam (1970).

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Transport of sugars by the fat body of the silkworm, Bombyx mori

The transport of glucose and α-methyl glucoside into the fat body of the silkworm, Bombyx mori L., has been studied. Glucose is transported into the tissue by a mechanism similar to facilitated diffusion and α-methyl glucoside by a diffusion process. The uptake of these sugars is neither energy dependent nor coupled to a phosphotransferase system.

Magnetic Field Due to the Self-Gravity-Induced Electric Polarization of a Rotating Massive Body

he notion of the gravity-induced electric field has been applied to an entire self-gravitating massive body. The resulting electric polarization of the otherwise neutral body, when taken in conjunction with the latter's rotation, is shown to generate an axial-magnetic field of the right type and order of magnitude for certain astrophysical objects. In the present treatment the electric polarization is calculated in the ion-continuum Thomas-Fermi approximation while the electrodynamics of the continuous medium is treated in the nonrelativistic approximation.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Two-Impurity Kondo Problem

The two-impurity Kondo problem is studied by use of perturbative scaling techniques. The physics is determined by the interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins and the Kondo effect. In particular, for a strong ferromagnetic RKKY interaction the susceptibility exhibits three structures as the temperature is lowered, corresponding to the ferromagnetic locking together of the two impurity spins followed by a two-stage freezing out of their local moments by the conduction electrons due to the Kondo effect.

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

Some Generalisations of the Time Minimising Assignment Problem

The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.